Enter two integers, then click Calculate.

The extended Euclidean algorithm is an extension of the Euclidean algorithm that computes the greatest common divisor (GCD) of two integers a and b, and also finds the Bézout coefficients x and y such that a·x + b·y = GCD(a, b). This algorithm is fundamental in number theory and cryptography. It is used for solving linear Diophantine equations, computing modular inverses, and in the RSA encryption algorithm. The method works by repeated division and back-substitution. This calculator provides a step-by-step visualization of the algorithm, showing how the quotients and remainders are computed. Understanding the extended Euclidean algorithm is essential for advanced mathematics, computer science, and cybersecurity applications.

1. Enter the first integer a.
2. Enter the second integer b.
3. Click Calculate to find the GCD and Bézout coefficients.
4. The result shows the GCD, coefficients x and y, and a step-by-step calculation.
5. Click Reset to restore default example values.